An objective calculation for ranking NCAA Division 1 FBS football teams based only on wins per game of the team, of their opponents, and of the opponents' opponents.

Sunday, October 4, 2009

Explanation of the Calculation

The only values used in the calculation are:

When the team plays a game (G)

Whether the team wins (W)

The wins per game of the team’s FBS opponent

The collective wins per game of the opponent’s FBS opponents

Each game a team plays, generates a quotient (Q) that is theoretically between 0-200 with the average 100, more than 100 is above average, and less than 100 is below average.

For the season, the average quotient per game is used to rank the team’s performance.

The equation for the quotient for each game for an FBS opponent:

Q = 100*{W+(∑Wo-1+W)/(∑Go-G)*[(∑Woo-∑W)/(∑Goo-∑G)+0.5]}

Q = the quotient for that game

G = 1, when a game has been played

W = 1, when the team won the game. W = 0, when it loses.

Go = the games played against FBS opponents by that opponent

Wo = the wins over FBS opponents of that opponent

Goo = the games played by the collective FBS opponents of that opponent

Woo = the wins of the collective FBS opponents of that opponent

The equation for a non-FBS opponent:

Q = 100*W

Explanation of each component of the equation:

Q = 100*{W+[(∑Wo-1+W)/(∑Go-G)]*[(∑Woo-∑W)/(∑Goo-∑G)+0.5]}

The orange 100 is used as a multiplier only to decrease the use of decimals. It converts the average number from 1.00 to 100 which makes it easier to comprehend for most people and less complicated when the numbers are put into lists.

The values in red are corrections used to subtract the result of each game from the opponent’s record and to subtract the team’s own record from their opponent’s opponents record for the calculation. This way the team is not rewarded for losing or having a losing record.

The green,W,is the result for the game itself, 1 (win) or 0 (loss).

The blue value is essentially the opponent’s record, ∑Wo/∑Go. The opponent’s record will vary from 0.00 (for a winless team) to 1.00 (for an undefeated team) with 0.50 the average. This is added onto the W so the value for the game varies from 0.00 for a loss to a team that has no other wins to 2.00 for a win over a team that otherwise was undefeated. A loss to an undefeated team is equal to a win over a winless team, 1.00.

The purple values are essentially the collective record of the opponent's opponents, ∑Woo/∑Goo. When this value is used as a multiplier for the opponent's record to give more strength when their opponents have a better record. The record would range from 0.00 to 1.00 with the average 0.50, but I add 0.50 so that this value ranges from 0.5 to 1.5 with the average 1.0. That way if the record of the opponent's opponents is average, multiplying by 1.00 leaves the opponent’s record unchanged.

For games against non-FBS opponents, the Wo, Go, Woo, and Goo are set at zero.